you now belong to a math club that has accumulated some valuable property (calculators, computers, etc.) that is kepts in a secure place under...

you now belong to a math club that has accumulated some valuable property (calculators, computers, etc.) that is kepts in a secure place under lock(s) and key(s). For security reasons you want at least two of you 12 club members present when the room is opened. To insure this, you put mulitple locks on the door and distribute keys to members so that no one member can open the room, but any two members can. Each lock has a different key, but you can make several copies of the same key to distribute to the club members. What is the fewest number of locks and keys that you will need?

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